Answer
Yes, f(x) is one-to-one.
Work Step by Step
The function $f(x)=\frac{1}{x}$ is one-to-one because it passes the horizontal line test (odd function). We can show this algebraically:
We start with the assumption that:
$x_1\ne x_2$
Then:
$\frac{1}{x_1}\ne \frac{1}{x_2}$
(Since taking the reciprocal of a unique number results in a unique number.)
So the function would not have the same $y$ value for two different $x$ values (one-to-one).
